Common Mistakes
Statistics · AP · Inference for Categorical Data — Chi-Square
Focus
Carrying Out a Chi-Square Test for Homogeneity or Independence
This topic is assessed on the AP Exam.
Frequent mistakes
### 1. Inference without conditions
What it looks/sounds like: Calculator p-value or CI is reported with no plan step.
Why it happens: Conditions feel optional on technology items.
How to fix: Always state Random, 10%, and Large Counts/Normality as applicable.
### 2. Wrong χ² procedure
What it looks/sounds like: Proportions z-test used instead of χ².
Why it happens: GOF vs homogeneity vs independence is mixed up.
How to fix: Match table layout to the correct χ² test.
### 3. Expected counts ignored
What it looks/sounds like: χ² is computed without checking expected counts.
Why it happens: Calculator output is trusted blindly.
How to fix: Verify expected counts ≥ 5 (or course rule) in each cell.
### 4. Correct work, wrong question
What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.
Why it happens: Attention locks onto the first operation instead of the final ask.
How to fix: Underline the final question; after solving, verify the boxed answer matches it.
### 5. Notation and justification gaps
What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.
Why it happens: Notation is treated as decoration rather than part of the score.
How to fix: Add one justification phrase per major step (definition, theorem, or rule).
How to avoid them
1. State hypotheses about distributions or association. 2. Report which cells contribute most to χ². 3. Conclude about the population in context.
Quick self-check
- [ ] Can pick the correct χ² test
- [ ] Can check expected counts
- [ ] Can conclude about association